Assuming only an undergraduate-level background in mathematics, this book explains the power of thinking probabilistically through a diverse set of applications drawn from science. It covers a wide range of topics never before discussed together in a unified fashion while keeping technicalities to a minimum.
Inhaltsverzeichnis
1. Introduction; 2. Random walks; 3. Langevin and Focker-Planck equations and their applications; 4. Escape over a barrier; 5. Noise; 6. Generalized central limit theorem and extreme value statistics; 7. Anomalous diff usion; 8. Random matrix theory; 9. Percolation theory; Appendix A. Review of basic probability concepts and common distributions; Appendix B. A brief linear algebra reminder, and some Gaussian integrals; Appendix C. Contour integration and Fourier transform refresher; Appendix D. Review of Newtonian mechanics, basic statistical mechanics and Hessians; Appendix E. Minimizing functionals, the divergence theorem and saddle point approximations; Appendix F. Notation, notation...; References; Index.
